Problem: $\dfrac{ 4h + 7i }{ 5 } = \dfrac{ 2h - 10j }{ -3 }$ Solve for $h$.
Answer: Multiply both sides by the left denominator. $\dfrac{ 4h + 7i }{ {5} } = \dfrac{ 2h - 10j }{ -3 }$ ${5} \cdot \dfrac{ 4h + 7i }{ {5} } = {5} \cdot \dfrac{ 2h - 10j }{ -3 }$ $4h + 7i = {5} \cdot \dfrac { 2h - 10j }{ -3 }$ Multiply both sides by the right denominator. $4h + 7i = 5 \cdot \dfrac{ 2h - 10j }{ -{3} }$ $-{3} \cdot \left( 4h + 7i \right) = -{3} \cdot 5 \cdot \dfrac{ 2h - 10j }{ -{3} }$ $-{3} \cdot \left( 4h + 7i \right) = 5 \cdot \left( 2h - 10j \right)$ Distribute both sides $-{3} \cdot \left( 4h + 7i \right) = {5} \cdot \left( 2h - 10j \right)$ $-{12}h - {21}i = {10}h - {50}j$ Combine $h$ terms on the left. $-{12h} - 21i = {10h} - 50j$ $-{22h} - 21i = -50j$ Move the $i$ term to the right. $-22h - {21i} = -50j$ $-22h = -50j + {21i}$ Isolate $h$ by dividing both sides by its coefficient. $-{22}h = -50j + 21i$ $h = \dfrac{ -50j + 21i }{ -{22} }$ Swap signs so the denominator isn't negative. $h = \dfrac{ {50}j - {21}i }{ {22} }$